Non Local Strain Gradient Cohesive Zone Formulation for Microvia Corner Step Debonding
Non-local strain gradient cohesive zone modeling eliminates mesh-dependent stress singularities at microvia corner steps to accurately predict reflow debonding.
Nanoindentation Size Effect
Meaning
Mechanical phenomena describe the trend where the measured hardness of a material increases as the depth of the indentation probe decreases. The nanoindentation size effect occurs because the volume of the plastic zone under the indenter scales differently than the surface area at very small depths. Understanding this behavior is essential for accurately characterizing the properties of thin films and surface treatments.
Load Sensitivity
Geometric imperfections at the very apex of the indenter can lead to inaccurate measurements at extremely low loads. If the radius of the tip is comparable to the depth of the indent, the nanoindentation size effect might be exaggerated or masked by the changing contact area. Regular calibration against standard materials like fused silica is required to separate the true material behavior from the artifacts caused by the probe shape.
Material Resistance
Strain gradients under a sharp indenter tip force the creation of additional crystal defects to accommodate the shape change of the material. A large portion of the nanoindentation size effect is driven by these dislocations, which provide extra resistance to deformation as the indentation becomes shallower. As the depth increases, the density of these dislocations drops and the hardness value converges toward the bulk material property.
Hardness Interpretation
Standardized testing protocols must specify the depth or the load at which a hardness value is reported to ensure comparability between different samples. Failure to account for the nanoindentation size effect can lead to an overestimation of the durability of a coating in real-world applications. Quality control laboratories in the semiconductor industry rely on mathematical models to extrapolate bulk properties from these superficial measurements.